ABSTRACT
This chapter aims to study the corresponding properties of Lorentzian distance and shows how the Lorentzian distance is related to the causal structure of the given space-time. It also shows that Lorentzian distance preserving maps of a strongly causal space-time onto itself are diffeomorphisms which preserve the metric tensor. G. Galloway shows that this concept of stability gives the control needed to force convergence arguments to be successful and hence obtains the theorem that for any compact Lorentzian manifold, each stable free timelike homotopy class contains a longest closed timelike curve which is of necessity a closed timelike geodesic. Galloway also shows how his result may be used to recover Tipler’s Theorem and gives a criterion for a free homotopy class of closed timelike curves to be stable.
